1 citations · 3 across the 9 of their papers we have counts for
9 papers · 1 filter
On Hamilton Decompositions
Dhananjay P. Mehendale
P. J. Kelly conjectured in 1968 that every diregular tournament on (2n+1) points can be decomposed in directed Hamilton circuits [1]. We define so called leading diregular tourname…
On Caccetta-Haggkvist Conjecture
Dhananjay P. Mehendale
We show that we cannot avoid the existence of at least one directed circuit of length less than or equal to (n/r) in a digraph on n vertices with out-degree greater than or equal t…
Ising Problem on Simple Cubic Lattice
Dhananjay P. Mehendale
Simple cubic lattice (SC lattice) can be viewed as plane triangular lattice (PT lattice) by viewing it along its principle diagonal lines. By viewing thus we establish the exact on…
On Hadwiger Conjecture
Dhananjay P. Mehendale
We propose an algorithm to reduce a k-chromatic graph to a complete graph of largest possible order through a well defined sequence of contractions. We introduce a new matrix calle…
On the Theory of Colorful Graphs
Dhananjay P. Mehendale
The theory of colorful graphs can be developed by working in Galois field modulo (p), p > 2 and a prime number. The paper proposes a program of possible conversion of graph theory…
Some Observations on the 3x+1 Problem
Dhananjay P. Mehendale
We present some interesting observations on the 3x+1 problem. We propose a new algorithm which eliminates certain steps while we check the action of 3x+1 procedure on a number. Als…